Before Chicago's 2-1 win over Toronto, Williams said he had volunteered to step down from his post several times.
"I offered it because, listen, I'm a big believer in self-analysis and self-assessment," Williams said. "I have a perspective that is one of needing, not wanting, needing this organization to be amongst the best in baseball. Another world championship puts you on the map, in my opinion, as an organization that stands and speaks for something. And that's what I wanted. That's what I still want out of my tenure here."
Williams was pressed on the issue, asked when he had offered his resignation, and he responded, "One year ago, six months ago, four months, three weeks ago, two weeks ago."
According to Williams, board chairman Jerry Reinsdorf talked him into staying on, telling Williams that he didn't like the idea of moving him to a different post in the organization.
"If I'm the cog in the machine that is tripping us up and my decisions are such now that they don't warrant, or my style doesn't warrant more opportunities to get that done, that's fine," Williams said. "I've been sitting in this chair for a long time anyway.
"I think I've told you guys before that there comes a time where everyone has an expiration date. I can accept that. But I'd still like to be a part of building something and hope that it can transition into that. If it doesn't, it doesn't, and you move on. But for now, I'm a White Sox, and I want another banner up there."
Williams said at the end of the day, he wants to do what's best for the organization.
"I felt compelled to reiterate again that I was completely prepared to vacate the seat," Williams said.
"And I even expounded on that by telling him if, in fact, it was his feeling that Ozzie and I needed to work together, I had no problems along those lines. Do I wish certain things had been done differently and handled differently? Absolutely. But I would have gone into it committed to making it work for the betterment of the Chicago White Sox."